Question 1

A proton (charge $$q = +1.6 	imes 10$$^{-19}$$ C, mass m = 1.67$$ 	imes $$10^{-27} kg) is $$initially located equidistant from two fixed point charges $$Q = +1.00 	imes 10$$^{-12}$$ C, each at a distance d_i = 5.00$$ 	imes $$10^{-6} m. $$What is the total electric potential at the proton's initial position due to both point charges? (Assume the potential at infinity is zero.)

Accepted Answer

$$V = 2k \frac{Q}{d_i}$$

Question 2

Given the same scenario as above, at what distance $$d_f$$ from either point charge will the proton momentarily come to rest, if it started with speed $$v_i = 1.00 	imes 10^6$ m/s?

Accepted Answer

$$d_f = \left[ \frac{2kQq}{mv_i^2$} + \frac{1}{d_i} \right]^{-1}$$

Question 3

After the proton reaches the point where it comes to rest, it accelerates away from the charges. What is its speed when it is very far from the charges ($$r 	o \infty$$)?

Accepted Answer

$$v = v_i$$

Question 4

For the circuit shown, what is the equivalent capacitance $$C_{eq}$$ between terminals A and B in terms of $$C_1$$, $$C_2$$, and $$C_3$$?

Accepted Answer

$$C_{eq} = \left( C_1$ + C_2$ \right) + C_3$

Question 5

If $$C_1 = 3.00$$\ \mu\mathrm{F}$$, C_2$ = 6.00\ \mu\mathrm{F}$$, $$C_3 = 4.00$$\ \mu\mathrm{F}$$, and V = 12.0$ V, what is the charge on C_3$?

Accepted Answer

$$Q_3 = 12.0$$\ \mu\mathrm{C}$$

Question 6

In the same circuit, what is the voltage across $$C_1$$?

Accepted Answer

$$V_1 = 4.0$ V

Question 7

If a dielectric with $$\kappa = 2.00 is $$inserted into $$C_3$$, what happens to the equivalent capacitance of the circuit?

Accepted Answer

It increases because $$C_3$$ doubles.

Question 8

A uniform wire with initial resistance $$R_0 = 9.0$$\ \Omega$$ is stretched to three times its original length, reducing its cross-sectional area to one-third. What is the new resistance?

Accepted Answer

$$R = 27\ \Omega$$

Question 9

A resistor $$R_1$$ dissipates power $$P$$ when connected to voltage $$V. A $$second resistor $$R_2$$ dissipates the same power $$P$$ when connected to $$2V. $$What is $$R_2 in $$terms of $$R_1$$?

Accepted Answer

$$R_2$$ = $$R_1/4$

Question 10

Which of the following correctly expresses the work done by a variable force $$\vec{F}$$ along a path from $$x_i to$$ $$x_f$$?

Accepted Answer

$$W = \int_{x_i}^{x_f} \vec{F} \cdot d\vec{x}$$

Question 11

A parallel-plate capacitor has area $$A$$ and separation $$d. If $$the area is tripled and the separation is doubled, what happens to the capacitance?

Accepted Answer

It increases by a factor of $$3/2.$$

Question 12

A hollow metal sphere of radius $$R$$ carries a total charge $$+Q. $$What is the electric potential at the center of the sphere, relative to infinity?

Accepted Answer

$$V = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q}{R}$$

Question 13

Which of the following is the correct expression for the electric field just outside a conductor with surface charge density $$\sigma$$?

Accepted Answer

$$E = \frac{\sigma}{\$$epsilon_0$$}$$

Question 14

A line of charge has linear charge density $$\lambda. $$What is the electric field a distance $$r$$ from the line?

Accepted Answer

$$E = \frac{\lambda}{2\pi\$$epsilon_0$$ r}$$

Question 15

Which of the following is the correct form of Gauss's Law for electric fields?

Accepted Answer

$$\Phi_{net} = \oint_S \vec{E} \cdot d\vec{A} = \frac{q_{enc}}{\$$epsilon_0$$}$$

Question 16

A current $$I$$ flows through a wire of cross-sectional area $$A$$ and charge carrier density $$n. $$What is the drift velocity $$v_d of $$the charge carriers?

Accepted Answer

$$v_d = \frac{I}{n e A}$$

Question 17

Which of the following correctly ranks the magnitude of the electric field between the plates in the three pairs shown (from greatest to least)?

Accepted Answer

3, then 1, then 2

Physics 1302W Quiz #2 Study Guidance: Electric Fields, Potential, Capacitance, and Circuits

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